Successful teaching

An interesting question was raised in one of my classes this week. The professor asked who in the room had ever had a calculus class. A handful of us raised our hands. I had it in both high school and college. He then assumed we all passed the class. I did, C in high school (if I remember right), and A in college. So was I successfully taught calculus?

What if I told you that at this point in my life I could recognize a calculus problem and probably tell you when calculus might be used to solve something, but I wouldn’t have the first idea of where to start solving it. Knowing that, was I successfully taught calculus? Was it pointless for me to take calculus then if 13-14 years later I can’t solve calculus problems? (I believe the answer to that is no. I also believe that is a whole other discussion.)

It also turns out that the answer to the majority of questions we were discussing that night was “it depends.” And as I left the class the professor called out for us to remember that, and I immediately quoted this poem:

so much depends
upon

a red wheel
barrow

glazed with rain
water

beside the white
chickens.
(The Red Wheelbarrow, William Carlos Williams)

That is a poem I learned my senior year of high school, also the year I took calculus in high school. Does that mean my English teacher a more successful teacher than my calculus teacher?

So how do you define successful teaching? A graduate class of teachers couldn’t decide on a definition. But I’m sure we will keep talking about it.